What is the Rössler attractor?

The Rössler attractor is a system of three coupled ordinary differential equations introduced by Otto Rössler in 1976: ẋ=−y−z, ẏ=x+ay, ż=b+z(x−c). With classical parameters a=b=0.2, c=5.7 it produces a strange attractor with a characteristic spiral-funnel topology.

How does it differ from the Lorenz attractor?

The Rössler attractor is simpler (only one nonlinear term, z·x) and has a single-scroll topology versus Lorenz's double-scroll. It also has a clear period-doubling route to chaos as parameter c increases, making it ideal for studying bifurcations.

What is the Lyapunov exponent of the Rössler system?

For classical parameters (a=b=0.2, c=5.7) the largest Lyapunov exponent λ₁ ≈ +0.071 b/s, confirming chaos. The sum λ₁+λ₂+λ₃ equals the phase-space divergence ∂ẋ/∂x+∂ẏ/∂y+∂ż/∂z = a−c+z, averaged over the attractor to ≈ −0.0 to −1.9, consistent with a dissipative system.

How do I interact with the simulation?

Drag the canvas to rotate the 3D view. Adjust sliders a, b, c to explore different regimes. Use preset buttons to jump between periodic and chaotic states. Toggle Auto-Rotate for hands-free 3D viewing.

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🧪 Rössler Chaotic Dynamics

Explore the Rössler attractor — a three-dimensional strange attractor defined by ẋ=−y−z, ẏ=x+ay, ż=b+z(x−c). Visualise period-doubling bifurcations, chaos, and sensitivity to initial conditions interactively.

Chaos & Dynamics2DModerate60 FPS

⚙ Under the hood

This simulation visualizes the Rössler attractor, a classic example of chaotic behavior in dynamical systems. It demonstrates how seemingly simple equations can generate complex and unpredictable patterns.

Rössler AttractorChaos TheoryNonlinear Dynamics

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install